a6_protocol.json

{
  "schema_version": 1,
  "protocol": "TCFM-A6-K1-record-solver-diagnostics-K2-freeze",
  "parent": {
    "proposal_sha256": "ea5462789c309d3f1418163db22f18aef51ec8bbf31427837090a769216018cf",
    "a1_a3_hf_commit": "249b01676f6495247107947efa8efb7dd414a03e",
    "a4_hf_commit": "c14d81233c46cfc6cf96d3ef67125137b161cb03",
    "a5_hf_commit": "13169d849f00fd52a7780c5d95528c095be0ddb9",
    "a5_addendum_sha256": "9945330678721301454948393f5757db6cc54a0587fa2fa6501533ce4d0bd4f2",
    "a5_scientific_source": "accca778ace03ae89c54cb792d01340bccab0796"
  },
  "retrospective_record": {
    "governs_prior_results": false,
    "campaign_protocol": "TCFM-A5-remediation-formal-H200",
    "scientific_source": "accca778ace03ae89c54cb792d01340bccab0796",
    "operator_sha256": "19c2d45026c0d06985ffcc8f3c90b21c01afb065a5f5c51db2931cc16ab4d3f2",
    "k1": {
      "status": "PASS",
      "closed_base_counts": {
        "stage_a": 36,
        "cont_ar": 12,
        "residual": 3
      },
      "report_path_basename": "k1_report_01.json",
      "report_sha256_reported_by_wandb": "b56d80d885832de1409b22cf32a656cd1934773eff2865b3ec284ed922f860f9",
      "wandb_run_id": "h200-a69bab0f649844fb96f4",
      "selected_arm": "rqs",
      "selected_tau": 0.05,
      "residual_mean_gain_nat_dim": 0.018253,
      "residual_interpretation": "passing the registered one-layer residual threshold does not prove that all remaining mismatch is unextractable or unlearnable",
      "eligible_rqs_mean_gap_nat_token": {
        "0.05": -3.278887,
        "0.1": -1.779094,
        "0.2": -0.489716
      }
    },
    "gj": {
      "status": "PASS",
      "report_path_basename": "gj_report_00.json",
      "report_sha256_reported_by_wandb": "bde84fdd4188a0495c523095c409cd34204738d906d830fa03e3beae5fc78510",
      "wandb_run_id": "h200-2d11e5685e65475a9322",
      "total_layer_passes": [
        2,
        4,
        6,
        8
      ],
      "pooled_token_match": [
        0.003594,
        0.008579,
        0.021423,
        0.04166
      ],
      "sequence_match_diagnostic": [
        0.0,
        0.0,
        0.0,
        0.0
      ],
      "sweeps_to_99": ">8",
      "interpretation": "plain Jacobi did not match the selected sequential inverse within eight registered layer-passes; this supports testing learned Stage B but is not proof that Stage B is sufficient or that every training-free solver fails",
      "formally_tested_tau": [
        0.05
      ],
      "does_not_establish_most_jacobi_resistant_tau": true
    }
  },
  "archive_precondition": {
    "required_before_a6_hf_freeze": true,
    "required_before_any_a6_gpu_child": true,
    "required_terminal_ledger_event": {
      "event": "operator_complete",
      "status": "GJ_PASS"
    },
    "service_must_be_exited": true,
    "active_lease_count": 0,
    "exact_k1_and_gj_report_sha256_must_match_record": true,
    "local_manifests_reports_and_ledger_are_authoritative": true,
    "wandb_is_supplementary_provenance": true,
    "a5_result_receipt_sha256": "707b7caade1de4e0f6a8d7bbf1d929c874154e2542ffde22428535c626885d95"
    ,
    "required_archive_members": [
      "TCFM/runs",
      "state",
      "operator",
      "README_H200_A5_REMEDIATION.md"
    ],
    "authoritative_h200_hours_source": "returned state/ledger.jsonl only",
    "required_narrative": [
      "formal K1 and G-J report records and every bound checkpoint SHA-256",
      "seed-level Stage-A, ContAR, residual, recovery, Jacobian-tail and G-J raw counts",
      "post-hoc H_implied table beside discrete anchor cross-entropy with units and approximation caveat",
      "one-layer residual gain separated from absolute Gaussianization or likelihood excess",
      "shadow-formal reconciliation"
    ],
    "h_implied_formula_exact": "H_implied=NLL_tok-d*log(tau)-(d/2)*log(2*pi*e), with d=16",
    "h_implied_role": "post-hoc zero-decision-weight small-tau sanity check, not a gate"
  },
  "shadow_formal_reconciliation": {
    "shadow_report_sha256": "5d175f3f0031e9d8bc4bb231deeb5ef3e4ee5bc786be64fd72ad8fb27ff07376",
    "shared": {
      "train_sha256": "f0af550932a7ae885647dffccf56a90a3f1a66987ef8c94eae2f1a8776760824",
      "val_sha256": "a7db6e9f93f4c36543883984d6b5dbf86ff4aa8aeddba6aa6e4a399cc1155b1c",
      "meta_sha256": "29493da221286fae15c6af3f897e79024619ec7eddb2e448bcb6df550ff7bb28",
      "evaluation_batch": 256,
      "evaluation_val_batches": 40,
      "evaluation_dequantization_seed": 12345,
      "evaluator_core_sha256": "376cc8c257a5e74ad754bf2ac51a97c62ffb7b5349c1cc3f9e562c96a7587fa8"
    },
    "shadow": {
      "hardware": "NVIDIA L40S",
      "source_commit": "db7cb945f4294628d0c9c6409ae1baf590b18417",
      "anchor_checkpoint_sha256": "82aa4b1da283e0e280a0e74277b116c819ec153ff3d850d623f86546be9bf71d",
      "embedding_sha256": "1937a6ff0971b8b82bcab75c67d65c35feba014c6fd8a79955e254f3bb10f658"
    },
    "formal": {
      "hardware": "NVIDIA H200",
      "source_commit": "accca778ace03ae89c54cb792d01340bccab0796",
      "anchor_checkpoint_sha256": "f97760007edf5c9a3c3675302b22594f77549a1b2769222ef97879a3c1e29602",
      "embedding_sha256": "39351baa0e4524d7e473074b344cd35ae85c6a6a6908348176fd3a60dc86b15c"
    },
    "formal_minus_shadow_gap_nat_token": {
      "0.05": 0.083442,
      "0.1": 0.376404,
      "0.2": -0.154975
    },
    "formal_gap_precision": "formal console values were available to six decimals; deltas are reported to six decimals",
    "same_checkpoint_bytes": false,
    "same_latent_inputs": false,
    "changes_formal_verdict": false,
    "evaluator_correctness_conclusion": "not_assessed_by_cross_campaign_comparison"
  },
  "solver_diagnostics": {
    "prospective": true,
    "formal_gate": false,
    "claim_weight": "zero",
    "changes_k1_or_gj_verdict": false,
    "authorizes_k2": false,
    "result_dependent_tuning": false,
    "must_complete_before_first_k2_training_child": true,
    "early_stopping": false,
    "selected_teacher_only": {
      "arm": "rqs",
      "tau": 0.05,
      "training_seeds": [
        0,
        1,
        2
      ],
      "stage_a_checkpoint_sha256_by_seed": {
        "0": "d23852a5235c45ac73e2763dbbe919aca34043e7db772478fa4cbf360d585e21",
        "1": "ae20a882cfedb02cf33108b3d6fe2aaa27e49d2e3ca8bfa5741b7a068bac52ac",
        "2": "4370393a5b12ec69da2f88f55b678bc98adfa91b66732695834bb7faacace547"
      },
      "residual_checkpoint_sha256_by_seed": {
        "0": "b2e2200ed8b03df2f69b5d17332fba80952fc0a50af6e22bfa2dfce5a3227dcc",
        "1": "ed3171ab361e57e9d138c689a180dd6a570e5901229340c4872cf241f320644d",
        "2": "75876cd49497848b2bd36c626de14c579e54b052b88b367806f9b10a8e5c04b3"
      },
      "manifest_records": "exact per-run config and manifest SHA-256 records in a5_result_receipt.json"
    },
    "source_seeds": [
      777,
      778,
      779
    ],
    "sequences_per_training_source_pair": 256,
    "sequence_length": 64,
    "dimensions_per_token": 16,
    "reference": "exact sequential Stage-A inverse",
    "metric": "pooled raw token-match counts over 3x3x256x64 tokens",
    "sequence_match_role": "diagnostic_only",
    "plain_jacobi_reference_total_layer_passes": [
      2,
      4,
      6,
      8
    ],
    "block_gs_jacobi": {
      "token_block_sizes": [
        4,
        8,
        16
      ],
      "block_order": "contiguous left-to-right",
      "within_block_update": "for the active token block, run frozen StageALayer.params on the complete current [B,64,16] estimate, apply the analytic RQS inverse to obtain a complete proposal, and write back only the active block; all coordinates in the block use the previous within-block iterate",
      "between_block_update": "Gauss-Seidel use of freshly updated preceding blocks",
      "identity_initialization": "x := layer_input",
      "layer_order": "invert frozen model.layers[1] and then model.layers[0], exactly the reverse of forward execution",
      "jacobi_updates_per_group": [
        1,
        2,
        3,
        4
      ],
      "one_block_update_cost": "one dense full-sequence StageALayer.params evaluation on all 64 tokens plus one full-tensor analytic RQS inverse; only the active block is committed",
      "serial_dependency_rounds": "2*(64/block_size)*jacobi_updates_per_group",
      "total_model_invocations": "2*(64/block_size)*jacobi_updates_per_group; every invocation is on the complete 64-token tensor",
      "serial_rounds_at_one_update_per_group": {
        "4": 32,
        "8": 16,
        "16": 8
      },
      "eight_round_interpretation": "block_size=16 with one update per group has eight serial block rounds, but it is not all-token parallel and is therefore not eligible to reverse formal G-J; every block-GS row is a hybrid K3 latency baseline",
      "required_reporting": [
        "token_match_at_every_block_update",
        "critical_path_layer_evaluations",
        "total_work",
        "model_invocations",
        "profiler_flops",
        "cuda_event_latency_seconds",
        "warmup_and_timing_protocol",
        "peak_vram"
      ],
      "timing": {
        "warmup_repetitions": 3,
        "measured_repetitions": 10,
        "synchronize_before_and_after": true,
        "statistic": "median CUDA-event seconds; also report all ten values"
      }
    },
    "selective_layer_jacobi": {
      "attribution": "adaptation of arXiv:2505.24791v2, revised 2026-05-04",
      "fully_frozen_local_definition_controls": true,
      "first_inverted_layer": "frozen model.layers[1], the first layer encountered in reverse execution, inverted by the unmodified StageALayer.seq_inverse implementation",
      "exact_update_order": "tokens i=0..63, and within each token scalar coordinates j=0..15",
      "exact_execution_cost": "for every token i, recompute the trunk on the complete current 64-token estimate; for every scalar j, execute MADE and analytic RQS inverse; no cache, pruning, sparse shortcut, or early stop is allowed",
      "remaining_layer": "frozen model.layers[0], inverted by unmodified StageALayer.jacobi_sweep with 1,2,4,8 sweeps",
      "identity_initialization": true,
      "early_stopping": false,
      "fully_parallel": false,
      "eligible_to_reverse_original_gj": false,
      "one_exact_sequential_layer": true,
      "required_reporting": [
        "token_match",
        "sequential_scalar_steps",
        "Jacobi_layer_passes",
        "model_invocations",
        "profiler_flops",
        "cuda_event_latency_seconds",
        "warmup_and_timing_protocol",
        "peak_vram"
      ],
      "timing": {
        "warmup_repetitions": 3,
        "measured_repetitions": 10,
        "synchronize_before_and_after": true,
        "statistic": "median CUDA-event seconds; also report all ten values"
      }
    },
    "interpretation": {
      "equal_cost_challenge_requires_token_match": 0.99,
      "equal_cost_challenge_requires_fully_parallel": true,
      "equal_cost_max_total_layer_passes": 8,
      "in_budget_fully_parallel_hit_at_0.99": "narrow the paper claim to plain-Jacobi failure and require K3 to beat this solver; do not alter the frozen G-J PASS",
      "stronger_out_of_budget_hit_at_0.99": "require K3 to include and beat the method at matched latency; do not describe it as an <=8 fully parallel solver and do not alter the frozen G-J PASS",
      "exact_sequential_hybrid_hit_at_0.99": "require K3 to include and beat the hybrid at matched latency; disclose its exact sequential layer and do not alter the frozen G-J PASS"
    },
    "output": {
      "separate_root_from_a5_formal": true,
      "versioned_immutable_json": true,
      "bind_final_k1_report_and_gj_report_sha256": true,
      "bind_three_stage_a_and_three_residual_checkpoint_records": true,
      "bind_code_data_embedding_anchor_hardware_and_timing": true
      ,
      "bind_decoder_and_identical_source_tensor_records": true
    }
  },
  "k2": {
    "prospective": true,
    "hardware": "NVIDIA H200",
    "incremental_budget_h200_hours_including_a6_diagnostics": 50.0,
    "cells": [
      "independent_full",
      "independent_prefix",
      "triangular_full",
      "triangular_prefix"
    ],
    "training_seeds": [
      0,
      1,
      2
    ],
    "required_run_count": 12,
    "representation": {
      "sequence_length": 64,
      "dimensions_per_token": 16,
      "tau": 0.05,
      "formal_embedding_sha256": "39351baa0e4524d7e473074b344cd35ae85c6a6a6908348176fd3a60dc86b15c",
      "train_dataset_sequences": 3125000,
      "train_data_sha256": "f0af550932a7ae885647dffccf56a90a3f1a66987ef8c94eae2f1a8776760824",
      "val_data_sha256": "a7db6e9f93f4c36543883984d6b5dbf86ff4aa8aeddba6aa6e4a399cc1155b1c",
      "data_meta_sha256": "29493da221286fae15c6af3f897e79024619ec7eddb2e448bcb6df550ff7bb28"
    },
    "couplings": {
      "data_latent": "X=E[token]+0.05*eta with eta an iid standard Gaussian tensor",
      "map_direction": "R_s maps data latent X to Gaussian endpoint epsilon",
      "independent": "epsilon is an iid standard Gaussian tensor independent of X",
      "triangular": "epsilon=R_s(X), using the selected RQS tau=0.05 Stage-A checkpoint matched to training seed s; the residual model qualifies but is not composed into R",
      "interpolation": "Z_t=(1-t)*epsilon+t*X",
      "velocity_target": "U=X-epsilon",
      "student_input_and_output": "v_theta receives (Z_t,t) and returns shape [B,64,16]",
      "training_loss": "FP32 mean of squared (v_theta(Z_t,t)-U) over batch, token, and scalar dimensions",
      "training_time_distribution": "one independent t~Uniform[0,1) per sequence; broadcast over its 64x16 scalars"
    },
    "architecture_matching": {
      "same_base_source_and_config_across_four_cells": true,
      "same_allocated_parameter_count": true,
      "same_active_parameter_count": true,
      "same_tensor_shapes_and_executed_dense_operations": true,
      "only_registered_architecture_difference": "the self-attention mask: inclusive token-causal for prefix versus bidirectional for full; endpoint coupling is the orthogonal experimental factor",
      "student": {
        "d_model": 576,
        "transformer_blocks": 8,
        "attention_heads": 8,
        "mlp_hidden": 2304,
        "within_token_hidden": 576,
        "normalization": "pre_layernorm",
        "activation": "GELU",
        "dropout": 0.0,
        "input_projection": "shared affine R^16->R^576",
        "position_embedding": "learned table [64,576] shared by all cells",
        "time_embedding": "fixed 128-vector [sin(omega_r*t),cos(omega_r*t)] for r=0..63, omega_r=2*pi*10^(3*r/63), followed by shared SiLU MLP 128->576->576 and added positionwise before block 1",
        "token_input": "the same unshifted Z_t token tensor is used in both architecture cells",
        "prefix_attention": "inclusive causal self-attention: trunk h_i may depend on complete token vectors Z_t[0:i+1] and may not depend on any token >i",
        "positionwise_paths": "LayerNorm, MLP, residual connections, position embedding and time embedding act independently at each token and cannot mix positions",
        "shared_dense_output_head": "a=GELU(A_h*h_i+A_z*z_i+A_t*e_t+b); v_i=B*a+C_h*h_i+C_z*z_i+c; all matrices are dense and identical in full and prefix cells, so every output coordinate may use all 16 coordinates of its current token",
        "full_attention": "bidirectional dense self-attention on the same unshifted input",
        "math_sdpa_only": true
      },
      "exact_source_commit_config_parameter_count_and_flop_receipt_required_before_first_run": true,
      "no_architecture_tuning_after_any_k2_metric": true
    },
    "training": {
      "steps": 30000,
      "batch_sequences": 256,
      "tokens_per_sequence": 64,
      "tokens_per_run": 491520000,
      "tokens_per_three_seed_cell": 1474560000,
      "tokens_all_12_runs": 5898240000,
      "optimizer": "AdamW",
      "adam_betas": [
        0.9,
        0.95
      ],
      "adam_epsilon": 1e-08,
      "weight_decay": 0.01,
      "learning_rate": 0.0003,
      "warmup_steps": 500,
      "learning_rate_schedule": "linear warmup lr*[(step+1)/500], then lr*[0.1+0.45*(1+cos(pi*(step-500)/(30000-500)))]",
      "gradient_clip": 1.0,
      "precision": "BF16 trunk with FP32 loss reduction",
      "checkpoint_for_decision": "final step 30000; no best-checkpoint selection",
      "strict_determinism": true,
      "seed_map": {
        "python_numpy_torch_and_loader": "s",
        "training_dequantization": "s+1",
        "independent_endpoint_gaussian": "3000+s",
        "time_sampling": "4000+s",
        "teacher_checkpoint": "s"
      },
      "pairing_and_schedule": {
        "schedule_file_by_seed": "schedule_s.npy with shape [30000,256], dtype little-endian uint32 and no pickle",
        "schedule_generation": "under torch 2.7.0 CPU, create one persistent torch.Generator seeded s; for each epoch call torch.randperm(3125000,generator=gen,dtype=int64), discard its final 8 indices (drop_last=true), concatenate epochs, truncate after 7680000 indices, cast to little-endian uint32 and reshape [30000,256]",
        "schedule_use": "all four cells for seed s load the same hash-bound schedule; no DataLoader shuffle, reshuffle, substitution, or skipped batch is permitted",
        "model_initialization": "generate one init_s state_dict under seed s before any run, hash-bind it, and load identical bytes into all four cells",
        "dequantization_stream": "a dedicated torch CUDA Generator seeded s+1; exactly one float32 randn [256,64,16] call per step",
        "time_stream": "a dedicated torch CUDA Generator seeded 4000+s; exactly one float32 rand [256,1,1] call per step",
        "independent_endpoint_stream": "a dedicated torch CUDA Generator seeded 3000+s; exactly one float32 randn [256,64,16] call per step in each independent cell",
        "lockstep_requirement": "within seed and coupling, full and prefix receive byte-identical dataset IDs, X, epsilon, t, Z_t and U at every step; X and t are also identical across the two couplings",
        "schedule_and_init_records_required_in_pre_run_receipt": true
      },
      "runtime": {
        "python": "3.10.x exact patch frozen in implementation receipt",
        "torch": "2.7.0+cu126",
        "numpy": "1.26.4",
        "cuda_runtime": "12.6",
        "cublas_workspace_config": ":4096:8",
        "pythonhashseed": "0",
        "allow_tf32": false,
        "deterministic_algorithms": true,
        "visible_gpu_count": 1,
        "gpu_name": "NVIDIA H200",
        "exact_driver_and_package_lock_required_in_pre_run_receipt": true
      },
      "attempt_policy": {
        "logical_identity": "(cell,training_seed)",
        "exactly_one_completed_attempt_per_identity": true,
        "completed_identity_must_never_rerun": true,
        "failed_attempts": "immutable, retained, zero decision weight, and fully charged to the budget",
        "retry": "only after the prior child, process group and lease are terminal; start from step 0 with identical source, config, schedule, init and random-stream seeds, without inspecting partial scientific metrics",
        "checkpoint_resume": false,
        "more_than_one_completed_attempt_or_any_parallel_duplicate": "protocol failure",
        "scientific_code_or_config_change_after_failure": "requires A7 before retry"
      },
      "teacher_target_construction_cost": "reported separately and excluded only from student-FLOP matching"
    },
    "evaluation": {
      "validation_batch_sequences": 256,
      "validation_batches": 40,
      "validation_sequences_per_seed": 10240,
      "validation_sequence_index_interval": "[10240,20480)",
      "evaluation_dequantization_seed": 12345,
      "independent_source_seed_by_training_seed": {
        "0": 777,
        "1": 778,
        "2": 779
      },
      "primary_uniform_t_grid": [
        0.0,
        0.06666666666666667,
        0.13333333333333333,
        0.2,
        0.26666666666666666,
        0.3333333333333333,
        0.4,
        0.4666666666666667,
        0.5333333333333333,
        0.6,
        0.6666666666666666,
        0.7333333333333333,
        0.8,
        0.8666666666666667,
        0.9333333333333333,
        1.0
      ],
      "early_t_diagnostic_grid": [
        0.0001,
        0.0003,
        0.001,
        0.003,
        0.01,
        0.03
      ],
      "early_t_points_enter_primary_thresholds": false,
      "risk_unit": "mean squared velocity error per scalar latent coordinate",
      "integrated_risk_estimator": "composite trapezoidal rule over the 16 primary t points after averaging all validation sequences and scalar coordinates",
      "paired_full_prefix": true,
      "pairing": {
        "x_tensor": "generate one FP32 eval_x tensor from validation indices 10240..20479, the frozen embedding and a dedicated torch CUDA Generator seeded 12345; all cells and seeds use its byte-identical hash-bound bytes",
        "independent_epsilon": "for seed s, generate one FP32 tensor with a dedicated torch CUDA Generator seeded 777+s; independent full and prefix use byte-identical bytes",
        "triangular_epsilon": "for seed s, compute R_s(eval_x) in FP32 with the frozen seed-matched teacher; triangular full and prefix use byte-identical bytes",
        "tensor_records": "eval_x, three independent epsilon tensors, and three triangular epsilon tensors are immutable little-endian float32 .npy files whose path, shape, bytes and SHA-256 are frozen in the pre-run receipt and bound into the report",
        "primary_time_construction": "form each k/15 in FP64, cast once to FP32, then compute FP32 Z_t and U; full and prefix consume byte-identical endpoints at all 16 times",
        "early_time_construction": "cast each registered decimal from FP64 to FP32 and use the same endpoint files and pairing",
        "model_execution_and_risk": "BF16 trunk under the frozen autocast environment; output, target and squared error are FP32; sufficient-statistic sums and trapezoidal integration accumulate in FP64"
      },
      "store_per_sequence_per_t_sufficient_statistics": true
    },
    "statistics": {
      "g_definition": "g(c)=R(c,prefix)-R(c,full)",
      "independent_penalty_definition": "P_ind=g(independent)/R(independent,full)",
      "closed_gap_definition": "C_gap=1-g(triangular)/g(independent), defined only when pooled g(independent)>0",
      "undefined_domain": "any nonfinite risk or R(independent,full)<=0 makes P_ind and C_gap undefined; pooled g(independent)<=0 leaves P_ind numerically defined but failing the 0.05 condition, makes C_gap undefined, and is an automatic scientific non-advance",
      "point_estimate": "pool risk sums and scalar counts across the three seeds before forming ratios",
      "bootstrap_replicates": 10000,
      "bootstrap_seed": 20260812,
      "bootstrap": "paired hierarchical bootstrap: resample the three training-seed clusters with replacement; for every occurrence of a seed cluster independently resample 10240 whole sequences with replacement, and reuse that occurrence's sampled sequence indices in all four cells and at every t",
      "lcb": "conservative 95% percentile lower bound (2.5th percentile); any replicate with nonfinite risk, R(independent,full)<=0, or g(independent)<=0 contributes negative infinity",
      "inference_scope": "decision rule for the three frozen training seeds and frozen validation sample; not a population theorem over training seeds",
      "advance_requires": {
        "independent_penalty_at_least": 0.05,
        "closed_gap_point_at_least": 0.75,
        "closed_gap_lcb_strictly_greater_than": 0.5
      }
    },
    "analytic_companion": {
      "required_before_text_k2_report": true,
      "distribution": "zero-mean length-64 scalar Gaussian AR(1)",
      "order_mapping": "d=1 special case of the token-major K2 order; scalar index k is token k",
      "rho": [
        0.1,
        0.3
      ],
      "triangular_transport": "positive-diagonal Cholesky map",
      "analytic_definitions": {
        "covariance": "Sigma[i,j]=rho^abs(i-j)",
        "independent_C_t": "C_t=(1-t)^2*I+t^2*Sigma",
        "independent_B_t": "B_t=t*Sigma-(1-t)*I",
        "independent_full_field": "A_full(t)=B_t*C_t^-1",
        "independent_prefix_field_row_k": "Cov(U_k,Z_t[0:k+1])*Cov(Z_t[0:k+1])^-1",
        "risk_formula": "with D=64 and architecture a in {full,prefix}, S_k^full={0,...,63}, S_k^prefix={0,...,k}; S_k^a is an index set, not a set complement. Define r_a(t)=D^-1*sum_{k=0}^{63}[Var(U_k)-Cov(U_k,Z_t[S_k^a])*Cov(Z_t[S_k^a])^-1*Cov(Z_t[S_k^a],U_k)] and R_a=(1/15)*[0.5*r_a(0)+sum_{h=1}^{14}r_a(h/15)+0.5*r_a(1)]. For each coupling q in {independent,triangular}, g_q=R_(q,prefix)-R_(q,full), and C_gap=1-g_triangular/g_independent when g_independent>0",
        "triangular_map": "X=T*epsilon for positive-diagonal Cholesky T, R=T^-1",
        "triangular_field": "v(z,t)=(T-I)*((1-t)*I+t*T)^-1*z; it is prefix-measurable and has zero Bayes risk"
      },
      "same_t_grids_and_risk_normalization": true,
      "fp64_requirements": {
        "triangular_full_risk_max": 1e-12,
        "triangular_prefix_risk_max": 1e-12,
        "abs_g_tri_max": 1e-12,
        "abs_c_gap_minus_one_max": 1e-10
      },
      "monte_carlo": {
        "samples": 262144,
        "seed": 20260812,
        "absolute_tolerance": 0.0005,
        "relative_tolerance": 0.02,
        "generator": "NumPy 1.26.4 Generator(PCG64DXSM(20260812)); store all generated standard-normal inputs as immutable little-endian float64 .npy files and bind their SHA-256 before evaluation",
        "cholesky": "numpy.linalg.cholesky in the exact implementation environment; output matrices and sampled tensors are hash-bound in the analytic receipt",
        "input_format_check": "emit the same per-sequence/per-t sufficient-statistic schema consumed by the text K2 aggregator and bootstrap"
      },
      "required_checks": [
        "analytic independent projection gap is positive",
        "analytic triangular prefix and full risks are both zero up to FP64 tolerance",
        "Monte Carlo estimates agree with analytic risks within a frozen implementation tolerance"
      ],
      "failure_effect": "invalidate the K2 evaluator; do not inspect or report a K2 gate verdict"
    },
    "dependency_smoke": {
      "required_before_first_k2_child": true,
      "autograd_test": "for random B=2,L=4,d=16 and every prefix output token i, gradients with respect to every coordinate of every input token >i must be bitwise zero",
      "finite_difference_test": "perturb each forbidden input and require bitwise-identical prefix outputs under FP64 CPU evaluation",
      "full_sanity": "the matched full cell must exhibit at least one finite nonzero future-coordinate derivative on the same deterministic fixture",
      "failure_effect": "protocol implementation failure; no K2 run starts"
    },
    "budget_enforcement": {
      "charge_every_gpu_child_and_failed_attempt": true,
      "check_remaining_before_each_child": true,
      "term_margin_seconds": 60,
      "kill_grace_seconds": 20,
      "independent_child_supervisor": true,
      "no_child_if_remaining_seconds_not_greater_than_term_margin": true
    },
    "reporting": {
      "versioned_immutable_json": true,
      "exact_12_run_closure": true,
      "bind_a6_hf_commit_protocol_source_data_embedding_teacher_checkpoints_configs_manifests_hardware_and_budget": true,
      "required_exact_hash_fields": [
        "addendum_A6_sha256",
        "a6_protocol_json_sha256",
        "a6_hf_commit",
        "a6_hf_readback_receipt_sha256",
        "a5_result_receipt_sha256",
        "implementation_source_commit",
        "implementation_code_manifest_sha256",
        "environment_lock_sha256",
        "full_config_sha256",
        "parameter_and_flop_receipt_sha256",
        "schedule_and_init_receipt_sha256",
        "evaluation_endpoint_receipt_sha256"
      ],
      "report_all_seed_level_and_t_level_risks": true,
      "no_silent_omission": true
    },
    "tracking": {
      "local_immutable_ledger_manifests_metrics_checkpoints_and_reports_are_authoritative": true,
      "wandb_online_is_supplementary_when_available": true,
      "network_or_wandb_failure_must_be_recorded_but_cannot_change_scientific_metrics_or_select_an_attempt": true,
      "offline_runs_must_be_synced_afterward_when_network_is_available": true
    }
  },
  "k3_and_exploratory": {
    "k3_forbidden_until_valid_k2_advance": true,
    "formal_k3_requires_later_operational_freeze": true,
    "formal_k3_must_include": [
      "direct one-shot student",
      "matched-inference-FLOPs deeper one-shot student",
      "shared multi-step student",
      "plain and strongest A6 training-free inverse baselines",
      "MDLM matched for training tokens, parameter scale, inference FLOPs, tokenizer, context, and evaluation budget",
      "causal autoregressive model with KV cache"
    ],
    "baseline_matching_disclosure": "every unavoidable MDLM or other baseline mismatch in tokenizer, context, training tokens, parameter scale, inference FLOPs, or evaluation budget must be reported explicitly",
    "post_verdict_zero_claim_diagnostics": [
      "ContAR with 512 Gaussian-mixture components",
      "plain/block-GS/selective inverse curves for RQS tau 0.05, 0.1, and 0.2"
    ],
    "exploratory_outputs_must_be_isolated": true,
    "exploratory_outputs_cannot_change_k1_ranking_k1_gj_or_k2": true
  },
  "implementation_freeze": {
    "first_exact_implementation_may_follow_addendum_commit_before_any_metric": true,
    "must_be_uploaded_and_read_back_before_diagnostics_or_k2": true,
    "must_match_a6_protocol_without_scientific_discretion": true,
    "changing_an_already_frozen_implementation_or_deviating_from_protocol_requires": "A7"
  }
}